Embedding non-differentiable black-box constraints into CCFM

Develop a version of Chance-constrained Flow Matching (CCFM) that can incorporate and enforce hard constraints specified by non-differentiable black-box simulators without closed-form expressions (for example, collision checkers and conserved invariants) in domains such as robotics and scientific simulation, integrating these constraints directly into the sampling process.

Background

The paper introduces Chance-constrained Flow Matching (CCFM), which enforces constraints during sampling by reformulating them via chance-constrained programming and deriving tractable deterministic projections, with examples primarily focused on constraints that admit closed-form expressions (e.g., linear or quadratic forms).

In the conclusion, the authors note that many real-world domains—particularly robotics and scientific simulation—often rely on constraints represented by non-differentiable black-box simulators, which lack closed-form expressions. They explicitly state that handling such constraints is out of scope and remains open, identifying the challenge of embedding black-box simulators within CCFM as a concrete unresolved direction.